G = 81gp6xC3 is Direct product 81gp6 x C_3
G has 3 minimal generators, rank 3 and exponent 27. The centre has rank 2.
The 13 maximal subgroups are: Ab(9,3,3), Ab(27,3) (3x), 81gp6 (9x).
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 3.
At present no information on the cohomology ring.